I’m curious if there is some grand equation, or if it is compounding complexity as the cord gets more and more tangled toward a “tangle equilibrium,” where it can’t get tangled anymore? Thanks!
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There is actually quite a bit of mathematics behind this and it even touches on physics as a model for a thermodynamic system reaching equilibrium. Every time the cord moves and crosses itself it can either start a new knot or it can untie an existing knot. The probability for each depend on the length of the cord, how stiff it is and how many knots are already on it. If there are no knots then any change will start a new knot. However over time there will be more knots and the movement of the chord will have an equal chance of creating a new knot or untying an existing knot. At that point the cord will not get any more tangled.
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